I think that Gin and Akai go a little deeper than what's on the surface. I remember Akai saying Gin's real name outloud after sniping him when the BO was targeting the Mouri detective agency.
If he knows Gin's real name it might mean they have a history, or otherwise just that Akai got a lot of information when he was undercover.
EDIT: Ok, nevermind. I decided to confirm this with the Wiki and it turned out Akai just called him "old enemy". Probably should've got my facts straight... But anyways, yeah I do think that Akai and Gin still got some history we don't know about.